Let $AB = 6$, $BC = 8$, and $AC = 10$. What is the area of the circumcircle of $\triangle ABC$ minus the area of the incircle of $\triangle ABC$?

eileenthecoolbean Jul 14, 2017

#1**+1 **

The radius of the cicumscribing circle is given by :

[ Product of the side lengrhs ] / [ 4 * Area of the triangle ] =

[ 6 * 8 * 10 ] / [ 4 (1/2) * 6 * 8] = 10 / 2 = 5 units

The radius of the incircle is given by

[ 2*Area of the triangle] / [Perimeter] = [ 2* (1/2) * 6 * 8] / [ 6 + 8 + 10] = 48 / 24 = 2 units

So....the area of the circumcircle - area of the incircle =

[pi] [5^2 - 2^2] = pi * [25 - 4] = 21pi units^2 ≈ 65.97 units^2

CPhill Jul 14, 2017